Killing an elephant most 'normal rifles' will do... eventually,as you saw.
Elephant guns and dangerous game rifles are what are designed for doing it as quickly as possible, yes preferably with one shot, especially if it is charging.
The legal minimums in africa to hunt elephant are the 9.3 x62 and 375H&H class of guns.
The real speciality dangerous game guns start with the 400cals, like the 416 remington, 416 weatherby, 416 rigby, 404 jeffery.
Up through the heavier guns such as the 458 winchester magnum, 460 weatherby, 470nitro etc.
To the most powerful rifles of all which are the true elephant guns or just called 'stopper rifles'
Like the 500 A-square, 577nitro express, 585 gehringer, 600overkill and 700nitro.
All of these will drop an elephant on the spot with a frontal or side brain shot, and kill them within a minute or less with a lung or hear shot from the side.
Its also possible to kill an elephant with a much smaller calibre, you just need to have very tough bullets(no hollowpoints and quickly expanding deer bullets and anti personal softpoints like the cops were probably using) and know where to hit it.
Most the problem is those guys blasting at it were shooting it in all the wrong places. If they knew where to aim they would have taken it a lot quicker.
As a side note 'the test of an elephant gun' is the frontal brain shot on elephant.Bullet has to get through about 18" of cellular/structured bone, and sinuses, plus possibly break the huge back superhard molars or tusk roots to make it to the brain.
To do that the minimums are a solid or FMJ bullet with a sectional density of .300 and a velocity of around 1800fps or more are needed.
Sectional density means weight per cross sectional area-very basically how loooong the bullet is. The longer it is for the calibre the more it penetrates.
This rules out almost all handguns/pistols, shotguns, most lever action cartridges since they have stubby bullets of sectional density usually around .15-.25 and even when they load very long heavy bullets velocity then is rarely above 1500-1700fps.
Its possible to kill elephants with a side brain shot much easier and some handguns and normal rifles with softpoints can do this.
I think if those cops had a regular issue 308 winchester in the trunk they should have been able to do a better job.
Couple of shots in the lungs, where its only skin and ribs protecting them, and it would have been finished a lot quicker